Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
int main(void)
{
	int i,n,j;
	double a;
	vector<double> x;
	cin>>n;
	for(i=0;i<n;i++)
	{
       double tp1;
       cin>>tp1;
       x.push_back(tp1);
    }
    

    sort(x.begin(),x.end());
    for(i=0;i<n;i++)
    
   
    
	a = ((double)x[n-1] + (double)x[n-2])/((double)x[1] - (double)x[0]);
    for(i=0;i<3;i++)
    {
       for(j=0;j<3-i;j++)
      {
		 for(int k=0;k<n-2;k++)
		{
			if(k+1==n-1-i||k+2==n-1-i||k+1==n-2-i-j||k+2==n-2-i-j)
			continue;
			double b = (x[n-i-1] + x[n-2-j-i])/(x[k+2] - x[k+1]);
			if(b>a)
               
			    a = b;
			
			
		
		}	
	 }
	}
	 printf("%f\n",a);
	return 0;
}